What kind of Domain should we use for our ecommerce site? Should it be A-Level domain, B-Level, or C-Level?

ecommerce sites should be a Top Level Domain , don`t forget to use SLL ( https)

Hello Sayan, I think you jumped into a far, tinny and a Questionable part of SEO, there are dozens of optimization steps to take before you start thinking of such an issue (for both fresh and old websites).
In my opinion, you should care about 3 main issues related to your new website ip (wither its an eCommerce or a blog):
1- Make sure the IP is dedicated (Not Shared).

2- Make sure the IP has no spam history.

3- Make sure the IP (or should I say server) is closest to your expected users/customers.
IP-Classes effect on SEO used to be a Myth by old-school SEO guys, saying that a link from a different C-class give you more value.
For me, you need to be a spammer - or a white hat SEO expert playing with fire to go that far! So dont care about classes, just make sure of the above 3 points and you will be fine, since its a new website, you have many more important things to start with before thinking of ip effect and back-links.
Good Luck!